Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Exact expanded first-order arithmetic statement
forall V L r s i d e. (((~((V)=0)) /\ (forall dpi_index_dpi_lookup_map dpi_row_dpi_lookup_map dpi_column_dpi_lookup_map. (exists pvs_gap_dpi_lookup_mapwindow. pvs_gap_dpi_lookup_mapwindow + S (dpi_index_dpi_lookup_map) = (L)) -> (exists pvs_gap_dpi_lookup_mapremainder. pvs_gap_dpi_lookup_mapremainder + S (dpi_column_dpi_lookup_map) = (V)) -> (dpi_index_dpi_lookup_map)=(V)*(dpi_row_dpi_lookup_map)+(dpi_column_dpi_lookup_map) -> (((exists ff_h_pvs_dpi_lookup_mapvalue. ff_h_pvs_dpi_lookup_mapvalue + S ((dpi_row_dpi_lookup_map)*(dpi_column_dpi_lookup_map)) = S ((S (dpi_index_dpi_lookup_map)) * s)) /\ exists ff_q_pvs_dpi_lookup_mapvalue. r = ff_q_pvs_dpi_lookup_mapvalue * S ((S (dpi_index_dpi_lookup_map)) * s) + ((dpi_row_dpi_lookup_map)*(dpi_column_dpi_lookup_map))))))) -> (exists pvs_gap_dpi_lookup_index. pvs_gap_dpi_lookup_index + S (i) = (L)) -> (exists pvs_gap_dpi_lookup_column. pvs_gap_dpi_lookup_column + S (e) = (V)) -> i=V*d+e -> (((exists ff_h_pvs_dpi_lookup_result. ff_h_pvs_dpi_lookup_result + S (d*e) = S ((S (i)) * s)) /\ exists ff_q_pvs_dpi_lookup_result. r = ff_q_pvs_dpi_lookup_result * S ((S (i)) * s) + (d*e)))Constructive proof overview
Generated structural guide
At supplied genuine row and bounded column coordinates, the actual beta code stores their product.
The unchanged tactic script uses 0 declared prerequisites and contains 19 exact native proof lines.
Alpha v34 checked-use · first admitted v32 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.